2000/02/22 by Nimish A. Shah
Mathematics · #math.RT #math.DG #msc:22E40
published as Proc. Indian Acad. Sci. Math. Sci. 106 (1996), no. 2, 105--125
arxiv created 2000/02/22 · arxiv updated 2009/11/30
Let L be a Lie group and Lambda a lattice in L. Suppose G is a non-compact simple Lie group realized as a Lie subgroup of L, and the image of G on L/Lambda is dense. Let c be a diagonalizable element of G not contained in a compact subgroup. Let U be the expanding horospherical subgroup of G associated to c. Let Omega be a nonempty open subset of U, and ni be a sequence of natural numbers tending to infinity. It is shown that the image of the union of the sets cni.Omega in L/Lambda is dense. A stronger measure theoretic formulation of this result is also obtained. Among other applications of the above result, we describe G-equivariant topological factors of the product space L/Lambda × G/P, where the real rank of G is greater than 1, P is a parabolic subgroup of G, and G acts diagonally. We also describe equivariant topological factors of unipotent flows on finite volume homogeneous spaces of Lie groups.